Such a handling system has been known from practice. It connects the spinning area with the storage area and has a transport means with a separating device in the spinning area. The transport means comprises a plurality of individual systems, namely, so-called doffers and an overhead monorail conveyor. The doffers have a displaceable and rotatable column, which is rail-borne on the floor and in the head area, with an individual pin for taking up a doff comprising a plurality of filament bobbins. The individual doffer can travel to and fro only in the aisle in front of the spinning frames set up in a row and it can transfer the doff to a carrier of the overhead monorail conveyor in the aisle area. This requires a plurality of doffers. During this transfer, which takes place in the spinning area, the filament bobbins are separated by the doffer and are attached to the carrier on the overhead monorail conveyor. The visual inspection of the individual filament bobbins also takes place in the spinning area. The second transport system then delivers the filament bobbins into the bay area, where they are transferred once again to a high-bay warehouse storage and retrieval system and are stored in a suitable manner. The prior-art technique has the drawback of requiring very much time and complicated apparatus and control engineering. The coordination of the two transport systems and the need that a carrier must be made ready in time for the loaded doffer are also problematic. The automation of the handling system is not always ensured as a result.